If events A and B are independent, the probability of both events occurring (the intersection of A and B, denoted as \( P(A \cap B) \)) can be calculated using the formula:
\[ P(A \cap B) = P(A) \times P(B) \]
Given \( P(A) = 0.32 \) and \( P(B) = 0.95 \), we can calculate:
\[ P(A \cap B) = 0.32 \times 0.95 \]
Calculating this gives:
\[ P(A \cap B) = 0.304 \]
Thus, rounding to the nearest thousandth, the value of \( P(A \cap B) \) is:
\[ \boxed{0.304} \]